A mathematical model for granulation kinetics

Abstract

An equation for granulation kinetics has been derived on the basis of the mass balance of the material being granulated. The model presented takes into account mechanisms that cause a decrease in the mass of granule-size groups, i.e. crushing and abrasion, and mechanisms which lead to an increase in size group mass, i.e. coalescence and layering. Considering a given group of size distributions, a rate of mass fraction growth was presented taking into account the influence of granules of both larger and smaller size. As a result a dependence describing the increase in the mass fraction of a size group has been obtained. The dependence contains three characteristic functions: a decrement rate function for a given size group, an agglomeration rate function, and a function of the growth rate of a given size group resulting from destroying large-size granules (grinding rate function). An experimental granulation of wet fine material in a drum has been performed. The obtained granule-size distributions were approximated by a frequency function of gamma distribution. Theoretical size distributions were the basis for determining characteristic rate functions in a kinetic equation. As a result, all rate functions were described for each size group in the system during the whole granulation investigated. These functions completely described the kinetics of the granulation process. A comparison of real and theoretical distributions (determined on the basis of the model) obtained in subsequent periods of the process gives a good agreement of the model with the real run of the process.